Source: Notre Dame J. Formal Logic
Volume 52, Number 3
Which abstraction principles are acceptable? A variety of criteria have been
proposed, in particular irenicity, stability, conservativeness, and
unboundedness. This note charts their logical relations. This answers some open
questions and corrects some old answers.
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 Boolos, G., "The standard of equality of numbers", pp. 234–54 in Meaning and Method: Essays in Honor of Hilary Putnam, edited by G. Boolos, Harvard University Press, Cambridge, 1995. Reprinted in [Boolos:1998?].
 Boolos, G., Logic, Logic, and Logic, edited by R. Jeffrey, Harvard University Press, Cambridge, 1998.
 Cook, R., “Conservativeness, stability, and abstraction,” forthcoming in the British Journal for Philosophy of Science.
 Hale, B., "Reals by abstraction. Abstraction and neo-logicism", Philosophia Mathematica. Series III, vol. 8 (2000), pp. 100–123.
 Hale, B., and C. Wright, The Reason's Proper Study. Essays towards a Neo-Fregean Philosophy of Mathematics, The Clarendon Press, New York, 2001.
 Linnebo, Ø., "Introduction [to a special issue on the bad company problem]", Synthese, vol. 170 (2009), pp. 321–29.
 Linnebo, Ø., and G. Uzquiano, "Which abstraction principles are acceptable? Some limitative results", The British Journal for the Philosophy of Science, vol. 60 (2009), pp. 239–52.
 Shapiro, S., "The company kept by cut abstraction (and its relatives)", Philosophia Mathematica, vol. 19 (2011), pp. 107–38.
 Shapiro, S., Foundations without Foundationalism. A Case for Second-Order Logic, vol. 17 of Oxford Science Publications, The Clarendon Press, New York, 1991.
 Shapiro, S., "Frege meets Dedekind: A neologicist treatment of real analysis", Notre Dame Journal of Formal Logic, vol. 41 (2000), pp. 335–64. Special Issue: Logicism and the Paradoxes: A Reappraisal, II.
 Uzquiano, G., "Bad company generalized", Synthese, vol. 170 (2009), pp. 331–47.
 Weir, A., "Neo-Fregeanism: An embarrassment of riches", Notre Dame Journal of Formal Logic, vol. 44 (2003), pp. 13–48.